This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for A Study of the Bruton's Tyrosine Kinase Inhibitor Ibrutinib Given in Combination With Bendamustine and Rituximab in Patients With Newly Diagnosed Mantle Cell Lymphoma (NCT01776840), a randomized phase 3 study. The primary outcome is Progression-free Survival (PFS).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01776840 |
| Phase | Phase 3 |
| Condition | Mantle Cell Lymphoma |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Enrollment | 523 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Janssen Research & Development, LLC |
| Results posted | Yes |
2. Clinical Question
Population
Patients 65 years of age or older with newly diagnosed mantle cell lymphoma. The registry reports an enrollment of 523 and describes the primary analysis population as the intent-to-treat set: all randomized participants classified according to assigned treatment, regardless of treatment actually received.
Intervention
Ibrutinib given in combination with bendamustine and rituximab. The intervention group is identified in the registry as Treatment B.
Comparator
Placebo given with bendamustine and rituximab. This is Treatment A, so the comparison concerns adding ibrutinib to the bendamustine-and-rituximab regimen rather than comparing entirely different treatment combinations.
Primary question
How did progression-free survival compare between the randomized groups? The endpoint counted the time from randomization to disease progression, relapse after complete response, or death, whichever occurred first. The reported comparison uses a hazard ratio and a log-rank test.
3. Trial Design
This was a randomized, double-blind, placebo-controlled phase 3 study with a parallel-group design. The registry describes masking as triple. Participants were assigned to either ibrutinib with bendamustine and rituximab or placebo with bendamustine and rituximab. The registry identifies the study population as patients 65 years of age or older with newly diagnosed mantle cell lymphoma.
The registry reports enrollment of 523. For the primary outcome, the posted arm counts are 262 for placebo with bendamustine and rituximab and 261 for ibrutinib with bendamustine and rituximab. The primary outcome population is described as intent-to-treat: randomized participants are analyzed according to assigned group, regardless of the treatment actually received. The record also gives the primary outcome timeframe as up to 97 months.
The study status is completed. The registry lists overall survival, complete response rate, time-to-next treatment, overall response, minimal residual disease-negative response, lymphoma-related quality-of-life worsening, duration of response, and duration of complete response among secondary outcomes. It reports 15 secondary outcome measures, although details of all outcome analyses are not available in the results.
The registry record does not report the trial’s original sample-size justification, the assumptions used to plan enrollment, or details of interim analyses. It also does not describe how randomization was generated or how allocation was concealed. Those omissions limit what can be said about design procedures beyond the stated randomized, masked, placebo-controlled parallel-group structure.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Before assignment: A total of 523 subjects were randomized in this study.
Overall Study
| Stage | Placebo + Bendamustine and Rituximab (BR) (Treatment A) | Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) |
|---|---|---|
| STARTED | 262 | 261 |
| Safety Analysis Set (Treated) | 260 | 259 |
| COMPLETED | 129 | 119 |
| NOT COMPLETED | 133 | 142 |
Reasons for not completing this period:
| Reason | Placebo + Bendamustine and Rituximab (BR) (Treatment A) | Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) |
|---|---|---|
| Lost to Follow-up | 12 | 7 |
| Withdrawal by Subject | 32 | 48 |
| Sponsor decision | 89 | 87 |
Analysis population for the primary outcome, as defined in the registry: Intent-to-treat (ITT) analysis set included all randomized participants and classified according to the assigned treatment group, regardless of the actual treatment received. Here, N (overall number of participants analyzed) signifies number of participants that were evaluable for this outcome measure.
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
| Characteristic | Unit | Placebo + Bendamustine and Rituximab (BR) (Treatment A) | Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) | Total |
|---|---|---|---|---|
| Participants analysed | 262 | 261 | 523 | |
| Age, Continuous | years | 71.7 (SD 5.2) | 71.8 (SD 5.04) | 71.7 (SD 5.12) |
| Age, Customized: 70 years and over | Participants | 154 | 162 | 316 |
| Age, Customized: < 70 years | Participants | 108 | 99 | 207 |
| Sex: Female, Male: Female | Participants | 76 | 83 | 159 |
| Sex: Female, Male: Male | Participants | 186 | 178 | 364 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 17 | 18 | 35 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 234 | 232 | 466 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 11 | 11 | 22 |
| Race/Ethnicity, Customized: American Indian or Alaska Native | Participants | 3 | 0 | 3 |
| Race/Ethnicity, Customized: Asian | Participants | 42 | 47 | 89 |
| Race/Ethnicity, Customized: Black or African American | Participants | 1 | 2 | 3 |
| Race/Ethnicity, Customized: Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race/Ethnicity, Customized: White | Participants | 206 | 199 | 405 |
| Race/Ethnicity, Customized: More than one race | Participants | 1 | 1 | 2 |
| Race/Ethnicity, Customized: Unknown or Not Reported | Participants | 9 | 10 | 19 |
| Race/Ethnicity, Customized: Other | Participants | 0 | 2 | 2 |
| Region of Enrollment: ARGENTINA | Participants | 0 | 4 | 4 |
| Region of Enrollment: AUSTRALIA | Participants | 12 | 19 | 31 |
| Region of Enrollment: BELGIUM | Participants | 10 | 5 | 15 |
| Region of Enrollment: BRAZIL | Participants | 10 | 11 | 21 |
| Region of Enrollment: CANADA | Participants | 7 | 4 | 11 |
| Region of Enrollment: CHINA | Participants | 26 | 31 | 57 |
| Region of Enrollment: CZECH REPUBLIC | Participants | 8 | 7 | 15 |
| Region of Enrollment: FRANCE | Participants | 13 | 8 | 21 |
| Region of Enrollment: GERMANY | Participants | 5 | 3 | 8 |
| Region of Enrollment: GREECE | Participants | 3 | 4 | 7 |
6. Primary Endpoint
The registry lists the primary outcome as Progression-free Survival (PFS), measured over Up to 97 months.
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | months |
| Endpoint classification | Time-to-Event Analysis |
The primary endpoint was progression-free survival, measured in months. It was defined as the interval from randomization until disease progression, relapse from complete response, or death, whichever was first reported. Disease assessments were based on the 2007 Revised Response Criteria for Malignant Lymphoma. The registry describes progression using the appearance of a new lesion or specified growth in previously involved sites.
Progression-free survival is a time-to-event endpoint: it uses both whether a qualifying event occurred and the time until that event. This can be useful when the clinical question concerns how long participants remain alive without recorded progression, rather than only whether a response was observed at a particular assessment. General statistical interpretation: a time-to-event analysis can account for participants whose event time is not observed during follow-up, provided the analysis appropriately handles censoring. The registry record does not report the censoring rules or details of follow-up procedures.
The registry reports median progression-free survival for each group and a hazard ratio for the group comparison. The median describes the time by which half of the analyzed group has experienced the endpoint, as estimated by the survival analysis. It is not the same as an average follow-up time or a guarantee about an individual participant’s outcome. The hazard ratio summarizes the relative event rate over follow-up under the model and assumptions used; it does not directly describe a difference in months for every participant.
7. Results Posted in the Registry
- Placebo + Bendamustine and Rituximab (BR) (Treatment A) vs Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B): hazard ratio 0.75 (95% CI 0.59–0.96), reported p = 0.011 (as reported in the registry).
Hazard ratio: Placebo + Bendamustine and Rituximab (BR) (Treatment A) vs Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B)
95% CI: 0.59 to 0.96
As reported in the registry
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Complete Response Rate | Binary Endpoint | Risk difference | +7.9 pts (-0.4 to 16.2) | 597 per arm |
| Percentage of Participants With Overall Response | Binary Endpoint | Risk difference | +1.1 pts (-4.2 to 6.4) | 12,470 per arm |
| Minimal Residual Disease (MRD)-Negative Response Rate | Binary Endpoint | Risk difference | +5.6 pts (-2.8 to 14.0) | 1,216 per arm |
Complete Response Rate
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B): 65.5% (171/261) versus 57.6% (151/262) on control; risk difference 7.9 percentage points (95% CI -0.4 to 16.2), risk ratio 1.14 (0.99–1.30); unadjusted two-proportion z-test p = 0.064.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) and the control. The interval gives the range of effects that remain compatible with the data.
Percentage of Participants With Overall Response
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B): 89.7% (234/261) versus 88.5% (232/262) on control; risk difference 1.1 percentage points (95% CI -4.2 to 6.4), risk ratio 1.01 (0.95–1.08); unadjusted two-proportion z-test p = 0.685.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) and the control. The interval gives the range of effects that remain compatible with the data.
Minimal Residual Disease (MRD)-Negative Response Rate
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B): 62.1% (162/261) versus 56.5% (148/262) on control; risk difference 5.6 percentage points (95% CI -2.8 to 14.0), risk ratio 1.10 (0.95–1.27); unadjusted two-proportion z-test p = 0.194.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) and the control. The interval gives the range of effects that remain compatible with the data.
Across the secondary outcomes with numerical comparisons available, the estimated percentages are directionally higher in the ibrutinib group. However, the unadjusted confidence intervals for the recalculated risk differences include no difference, and the unadjusted results are not reported as sponsor analyses. Taken together, these secondary findings are suggestive descriptions rather than firm confirmation of a broader pattern.
The primary endpoint and secondary endpoints address related but distinct questions. Progression-free survival measures time until progression, relapse after complete response, or death. Response outcomes describe the proportion meeting a response definition, while other listed outcomes concern survival, subsequent treatment, response duration, or patient-reported worsening. A consistent direction in some response percentages does not independently establish the primary time-to-event result, and the primary result does not settle every secondary question.
Many outcomes create a multiplicity issue: when several comparisons are examined, the chance of at least one apparently notable result can increase. General statistical explanation: a prespecified adjustment or hierarchical testing strategy can control the interpretation of multiple tests, but the registry record does not report such a strategy. The secondary p-values are explicitly unadjusted recalculations, so they carry less inferential weight than a primary analysis with a reported method and result.
The registry lists 15 secondary outcome measures, but the analysis details for every measure are not reported in the registry record. The available pattern should therefore be understood as limited to the numerical results that are posted, not as a complete synthesis of all secondary outcomes or all analyses conducted.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Overall Survival
- Complete Response Rate
- Time-to-Next Treatment
- Percentage of Participants With Overall Response
- Minimal Residual Disease (MRD)-Negative Response Rate
- Time to Worsening (TTW) in the Lymphoma (Lym) Subscale of the Functional Assessment of Cancer Therapy-Lymphoma (FACT-Lym) Questionnaire
- Duration of Response (DoR)
- Duration of Complete Response (DoCR)
9. Statistical Interpretation
The registry reports median progression-free survival of 52.9 months for placebo with bendamustine and rituximab and 80.6 months for ibrutinib with bendamustine and rituximab. The reported hazard ratio for Treatment A versus Treatment B is 0.75, with a 95% confidence interval from 0.59 to 0.96 and a log-rank p-value of 0.011. The registry classifies the reported analysis as a superiority analysis.
In this comparison, the hazard ratio is oriented as Treatment A versus Treatment B. Its reported value is below the no-difference reference for a hazard ratio, so its direction favors Treatment B for the progression-free survival event rate. The confidence interval also remains on that side of the reference. The p-value is the reported result of the log-rank test; it should be read as evidence against the test’s null hypothesis under that analysis, not as the probability that the null hypothesis is true or the probability that the observed result arose by chance.
The reported medians are consistent in direction with the hazard-ratio result: the median is longer in the ibrutinib group. These are group-level estimates, not descriptions of how every participant fared. The median confidence interval for Treatment A is 43.7 to 71.0 months. For Treatment B, the registry gives a lower confidence limit of 61.9 months but does not report an upper limit. The missing upper limit makes that median’s reported precision incomplete in the registry record.
The secondary outcomes with numerical comparisons show a less conclusive pattern. The posted percentage estimates are directionally higher in the ibrutinib group for complete response, overall response, and minimal residual disease-negative response. The corresponding unadjusted risk-difference confidence intervals include no difference, and the unadjusted p-values are 0.064, 0.685, and 0.194, respectively. These secondary findings do not have the same inferential standing as the reported primary analysis, particularly because multiplicity handling is not reported in the registry record.
These results describe the trial’s posted analyses; they do not establish what would happen to every patient, or how the groups would compare under circumstances not represented by the trial. They also do not resolve questions about outcomes or analyses that are not reported in the registry record.
10. Statistical Methods Explained
The primary result is a time-to-event comparison. Each participant’s progression-free survival time runs from randomization until the first qualifying event defined by the registry: disease progression, relapse from complete response, or death. General statistical explanation: time-to-event methods are designed for outcomes where both event occurrence and event timing matter. They can use information from participants who have not yet had a recorded event at the end of observed follow-up, but the validity of that approach depends on how censoring is defined and handled. Those details are not reported in the registry record.
What does the median describe?
The median is a summary of the estimated event-time distribution. It identifies the time by which half of the group is estimated to have experienced the endpoint. It does not mean that all participants had an event at that time, and it does not summarize the full shape of the survival curve. Two groups can have different medians while their event patterns vary in other ways over follow-up. The registry gives a median and confidence interval for Treatment A, and a median and lower confidence limit for Treatment B; an upper confidence limit for Treatment B is not reported in the registry record.
What does the hazard ratio summarize?
The registry reports a hazard ratio for Treatment A versus Treatment B. A hazard ratio compares event rates over the follow-up period, subject to the analysis model and its assumptions. The reported value of 0.75 is below the no-difference reference, indicating a direction that favors Treatment B for this endpoint. The 95% confidence interval, 0.59 to 0.96, describes uncertainty around the estimated comparison. It does not provide a range containing 95% of individual participant outcomes, and it does not show how long a particular participant will remain progression-free. The registry does not report diagnostics or other information that would allow the assumptions behind the hazard-ratio summary to be assessed.
How does the log-rank test fit in?
The reported comparison uses a log-rank test and gives a p-value of 0.011. General statistical explanation: the log-rank test compares event-time patterns between groups, taking account of the timing of events and the available follow-up. The p-value measures how compatible the observed test statistic is with the test’s null hypothesis under its assumptions. It is not a measure of the size or clinical importance of the difference. The hazard ratio and confidence interval communicate the estimated direction and precision, while the log-rank p-value addresses the test of the group comparison.
How should the secondary comparisons be understood?
The posted secondary percentages are accompanied by recalculated, unadjusted risk differences. A risk difference expresses the difference between group probabilities in percentage-point terms when probabilities are expressed as percentages. General statistical explanation: the confidence interval for a risk difference conveys uncertainty about the size and direction of that contrast. The posted intervals for the three secondary comparisons include no difference. Their unadjusted p-values do not account for the fact that many outcomes may be examined. No multiplicity adjustment is reported in the registry record, so these exploratory comparisons should not be treated as equivalent to a prespecified, multiplicity-controlled primary test.
The risk differences and associated intervals are recalculations from posted summary statistics, not the sponsor’s reported analyses. No sponsor analyses are listed for these secondary outcomes. They are descriptive statistical summaries and should not be mistaken for adjusted estimates or a complete account of the trial’s analysis plan.
What does the analysis population imply?
The primary outcome population is described as intent-to-treat. In general, this approach retains participants in the groups to which they were randomized, even if their treatment received differed from their assignment. It preserves the randomized comparison as defined by assignment. The registry says the set includes all randomized participants and that participants are classified according to assigned treatment, regardless of actual treatment received. The record does not provide a separate account of exclusions, missing outcome data, or how such data were addressed.
11. Confidence Intervals and Precision
The primary hazard-ratio estimate is 0.75, with a 95% confidence interval from 0.59 to 0.96. The interval stays below the no-difference reference for a hazard ratio, so the uncertainty represented by this interval is consistent with a lower event rate for Treatment B than Treatment A under the reported comparison. The range also shows that the estimated magnitude is not known with exactness. A confidence interval is an uncertainty range for an estimate under the statistical method; it is not a range of individual outcomes and does not guarantee that the true value lies inside it.
The registry reports median progression-free survival of 52.9 months for Treatment A, with a 95% confidence interval from 43.7 to 71.0 months. For Treatment B, it reports a median of 80.6 months and a lower confidence limit of 61.9 months, but no upper confidence limit. The incomplete interval for that median prevents a full comparison of median precision based on the registry entry alone. The hazard-ratio interval provides a separate summary of the group comparison and should not be substituted for the missing median limit.
The secondary risk-difference intervals are also relevant to precision. Each includes no difference, so the registry’s recalculated secondary estimates leave uncertainty about whether the group contrast is positive or negative. This does not prove that the groups are identical; it indicates that these estimates are not sufficiently precise to exclude no difference under the stated intervals. Their unadjusted status and the unreported multiplicity plan further limit the strength of conclusions drawn from them.
Precision depends on the amount and distribution of event information, follow-up, and the analysis method. The registry provides the primary outcome timeframe as up to 97 months, but detailed follow-up completeness and censoring information are not reported in the registry record.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect (log scale) | Hazard ratio | Events, 80% power | Events, 90% power |
|---|---|---|---|
| 100% of the observed effect | 0.75 | 380 | 508 |
| 75% of the observed effect | 0.81 | 675 | 903 |
| 50% of the observed effect | 0.87 | 1,518 | 2,032 |
The planning illustrations are not the trial’s original design calculations; the original sample-size assumptions are not reported in the registry record. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set as a stated fraction of the observed effect: 100%, 75%, or 50% of that effect. These calculations are planning illustrations, not observed power.
For the time-to-event endpoint, the planning figures are total event counts, not participants per arm. For the binary outcomes, the figures are participants per arm. The distinction matters: event-based planning depends on the number of events available for analysis, while participant-based planning describes the number of participants in each group needed under the stated assumptions.
The 80% power column gives the planning count associated with an 80% chance of detecting the specified effect if that effect and the calculation assumptions were correct. The 90% power column uses a higher target chance of detecting that same effect, which generally requires more information. These are design concepts, not probabilities that the reported trial result is correct.
Smaller effects are harder to distinguish from random variation, so the planning illustration requires more events or participants as the target effect is reduced from the full observed effect to 75% or 50% of it. The values depend on treating the observed effect as a starting point and on the stated simplified assumptions; they do not show what the trial was originally designed to detect or whether its actual conduct achieved a particular power.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.
Worked calculation for this trial
- Hazard ratio HR = 0.750, so ln(HR) = -0.2877.
- d = 4 × (1.96 + 0.842)2 / [ln(0.750)]2 = 379.4, rounded up to 380 events in total for 80% power.
The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).
R code
alpha <- 0.05
z_a <- qnorm(1 - alpha / 2) # two-sided
hr <- 0.75 # observed hazard ratio
events_needed <- function(power, frac = 1) ceiling(round(4 * (z_a + qnorm(power))^2 / log(hr^frac)^2, 6)) # Schoenfeld, 1:1 allocation
for (f in c(1, 0.75, 0.5))
cat(sprintf("%3.0f%% of observed effect: events = %s (80%% power), %s (90%% power)\n", 100 * f,
format(events_needed(0.80, f), big.mark = ","), format(events_needed(0.90, f), big.mark = ",")))
# Simulation: given d total events under proportional hazards, events in the treatment arm are Binomial(d, hr / (1 + hr)).
# The score (log-rank type) statistic is (D1 - d / 2) / sqrt(d / 4).
set.seed(1776840)
d <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))
Output from running the code
100% of observed effect: events = 380 (80% power), 508 (90% power)
75% of observed effect: events = 675 (80% power), 903 (90% power)
50% of observed effect: events = 1,518 (80% power), 2,032 (90% power)
Simulated power with 380 events: 0.787 (20000 replicates)
The simulation uses the fact that, with d events in total and proportional hazards, the number of events in the treatment arm is binomial. It is an approximation that conditions on the total number of events, and it should land close to the target power.
14. Group-Sequential Design Analysis
Many time-to-event trials, especially in oncology, stop or report early when interim data are overwhelming, so a single fixed-sample number understates the real design problem. The calculation below is an illustrative group-sequential design built from this trial's posted control median and hazard ratio. The registry record does not state the planned number of looks or the spending function, so the design is a planning illustration, not a reconstruction of the protocol. Assumed: one-sided α = 0.025, 90% power, three equally spaced looks on information, Lan-DeMets O'Brien-Fleming spending, 24 months of accrual, 60 months in total and a 1% monthly dropout hazard.
Under these assumptions the design needs about 1,515 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 23.6 | 172 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 38.3 | 343 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 515 | 1.993 | 0.0231 | 0.0250 |
Fixed design versus group-sequential alternatives
| Design | Power | Events at final analysis | Participants | Study length (months) |
|---|---|---|---|---|
| Fixed design, one analysis | 80% | 380 | 1,117 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 381 | 1,121 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 385 | 1,131 | 60.0 |
| Three looks, Pocock | 80% | 444 | 1,307 | 60.0 |
| Fixed design, one analysis | 90% | 509 | 1,498 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 511 | 1,503 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 515 | 1,515 | 60.0 |
| Three looks, Pocock | 90% | 588 | 1,729 | 60.0 |
Group-sequential designs cost a small increase in maximum sample size and events compared with the fixed design, in exchange for the chance to stop early for overwhelming efficacy. O'Brien-Fleming spending keeps early boundaries very conservative and the final boundary close to the fixed-design value, whereas Pocock spending spends more alpha early.
Sensitivity to a smaller true effect
Planning for exactly the observed effect is optimistic, because observed effects in published trials tend to be somewhat larger than the true effect. The table repeats the main design (three looks, O'Brien-Fleming spending, 90% power) for smaller true hazard ratios.
| True effect assumed | Hazard ratio | Events at final analysis | Participants |
|---|---|---|---|
| 100% of the observed effect | 0.750 | 515 | 1,515 |
| 75% of the observed effect | 0.806 | 915 | 2,622 |
| 50% of the observed effect | 0.866 | 2,056 | 5,742 |
For context, this trial enrolled 523 participants.
Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993. Agreement between the two packages confirms the boundary calculation.
R code and output
suppressWarnings(suppressMessages({ library(gsDesign); library(rpact) }))
med_control <- 52.9 # control-arm median, months (converted from the posted unit)
hr <- 0.75 # hazard ratio used for planning
lambdaC <- log(2) / med_control
eta <- 0.01 # dropout hazard per month (assumption)
acc_months <- 24 # accrual duration (assumption)
study_months<- 60 # total study duration (assumption)
design <- function(k, sfu, beta, h = hr) gsSurv(k = k, test.type = 1, alpha = 0.025, beta = beta, sfu = sfu,
lambdaC = lambdaC, hr = h, hr0 = 1, eta = eta, gamma = 1, R = acc_months, T = study_months, minfup = study_months - acc_months)
# Main design: 3 looks, Lan-DeMets O'Brien-Fleming spending, one-sided alpha 0.025, 90% power
x <- design(3, sfLDOF, 0.10)
cat(sprintf("N_TOTAL|%s\n", format(ceiling(sum(x$gamma * x$R)), big.mark = ",")))
for (i in 1:3) cat(sprintf("GS|%d|%.1f|%.0f|%.3f|%.5f|%.5f\n", i, x$T[i], x$n.I[i], x$upper$bound[i], pnorm(-x$upper$bound[i]), cumsum(x$upper$spend)[i]))
cat("\n"); print(gsBoundSummary(x))
# Comparison of designs
cmp <- list(list("Fixed design, one analysis", 1, sfLDOF), list("Two looks, O'Brien-Fleming", 2, sfLDOF),
list("Three looks, O'Brien-Fleming", 3, sfLDOF), list("Three looks, Pocock", 3, sfLDPocock))
cat("\n")
for (b in c(0.20, 0.10)) for (d in cmp) {
y <- design(d[[2]], d[[3]], b)
cat(sprintf("DES|%s|%d|%.0f|%s|%.1f\n", d[[1]], round(100 * (1 - b)), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ","), tail(y$T, 1)))
}
# Sensitivity: what if the true effect is smaller than the observed one? (3 looks, O'Brien-Fleming, 90% power)
cat("\n")
for (fr in c(1, 0.75, 0.5)) {
y <- design(3, sfLDOF, 0.10, exp(log(hr) * fr))
cat(sprintf("SENS|%.2f|%.3f|%.0f|%s\n", fr, exp(log(hr) * fr), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ",")))
}
# Independent cross-check of the boundaries with rpact
r <- getDesignGroupSequential(kMax = 3, alpha = 0.025, beta = 0.10, sided = 1, typeOfDesign = "asOF", informationRates = x$timing)
cat(sprintf("\nCross-check, upper boundaries: gsDesign %s | rpact %s\n", paste(round(x$upper$bound, 3), collapse = ", "), paste(round(r$criticalValues, 3), collapse = ", ")))
Method: LachinFoulkes
Analysis Value Efficacy
IA 1: 33% Z 3.7103
N: 1494 p (1-sided) 0.0001
Events: 172 ~HR at bound 0.5676
Month: 24 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.75 0.0338
IA 2: 67% Z 2.5114
N: 1516 p (1-sided) 0.0060
Events: 344 ~HR at bound 0.7626
Month: 38 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.75 0.5603
Final Z 1.9930
N: 1516 p (1-sided) 0.0231
Events: 516 ~HR at bound 0.8389
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.75 0.9000
Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993
15. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Log Rank | Hazard Ratio (HR) 0.75 | 0.59 to 0.96 | 0.011 |
The primary comparison is reported by the sponsor using a log-rank method. The registry gives a hazard ratio of 0.75, a 95% confidence interval from 0.59 to 0.96, and a p-value of 0.011, and labels the analysis as superiority. The primary time-to-event interpretation uses this reported analysis; it is not reconstructed from the posted medians.
The registry does not flag a discrepancy between the sponsor’s reported result and the calculated summaries. The sponsor’s own analysis therefore supplies the primary inferential result, while the other posted calculations are best treated as supporting descriptions rather than replacements for that analysis.
For the secondary outcomes discussed in the recalculations, the registry lists no sponsor-reported analyses. The risk differences and unadjusted p-values are simple comparisons recalculated from posted summary statistics. They should not be represented as sponsor-confirmed tests or as analyses adjusted for the trial’s full set of outcomes. The registry record does not report the sponsor’s complete statistical analysis plan, including any prespecified multiplicity strategy.
16. Multiplicity, Missing Data and Analysis Populations
The registry identifies progression-free survival as the primary outcome and reports a sponsor analysis using a log-rank test. It also lists numerous secondary outcomes, including overall survival, response measures, time-to-next treatment, response duration, and a patient-reported lymphoma subscale outcome. The record reports 15 secondary outcome measures, but it does not report a multiplicity adjustment, a hierarchy of tests, or another strategy for controlling interpretation across multiple outcomes.
This omission matters because separate tests across multiple outcomes can produce apparently notable results even when there is no underlying effect for those outcomes. The secondary risk-difference p-values in the recalculations are unadjusted; they should not be read as if they were protected against the multiplicity created by testing many outcomes. The registry does not report sponsor analyses for the secondary outcomes described in the recalculated comparisons.
The primary analysis population is stated to be intent-to-treat, including all randomized participants classified according to assigned group regardless of treatment received. That is useful information about the intended population for the primary comparison. However, the registry record does not report how missing outcome assessments were handled, what censoring rules were used, whether any participants were excluded from particular analyses, or how incomplete follow-up was addressed.
The record also does not report the full statistical analysis plan, the original sample-size justification, interim-analysis procedures, or any prespecified subgroup analyses. Their absence from the registry record does not show that these procedures were absent from the study; it means they cannot be evaluated from the reported information. These gaps limit assessment of how completely the posted results represent the planned analysis.
17. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo + Bendamustine and Rituximab (BR) (Treatment A) | 157 | 260 | 60.4% |
| Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) | 201 | 259 | 77.6% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Placebo + Bendamustine and Rituximab (BR) (Treatment A) | 129 of 262 |
| Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) | 120 of 261 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo + Bendamustine and Rituximab (BR) (Treatment A) | 255 of 260 |
| Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) | 256 of 259 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo + Bendamustine and Rituximab (BR) (Treatment A) | Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) |
|---|---|---|---|
| Pneumonia | Infections and infestations | 35 of 260 | 58 of 259 |
| Pyrexia | General disorders | 14 of 260 | 19 of 259 |
| Febrile Neutropenia | Blood and lymphatic system disorders | 9 of 260 | 16 of 259 |
| Atrial Fibrillation | Cardiac disorders | 4 of 260 | 14 of 259 |
| Sepsis | Infections and infestations | 6 of 260 | 10 of 259 |
| Cellulitis | Infections and infestations | 3 of 260 | 9 of 259 |
| Bronchitis | Infections and infestations | 4 of 260 | 7 of 259 |
| Diarrhoea | Gastrointestinal disorders | 2 of 260 | 8 of 259 |
| Covid-19 Pneumonia | Infections and infestations | 2 of 260 | 8 of 259 |
| Syncope | Nervous system disorders | 5 of 260 | 5 of 259 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo + Bendamustine and Rituximab (BR) (Treatment A) | Ibrutinib + Bendamustine and Rituximab (BR) (Treatment B) |
|---|---|---|---|
| Nausea | Gastrointestinal disorders | 107 of 260 | 109 of 259 |
| Diarrhoea | Gastrointestinal disorders | 96 of 260 | 119 of 259 |
| Neutropenia | Blood and lymphatic system disorders | 104 of 260 | 109 of 259 |
| Pyrexia | General disorders | 76 of 260 | 88 of 259 |
| Cough | Respiratory, thoracic and mediastinal disorders | 85 of 260 | 78 of 259 |
| Fatigue | General disorders | 77 of 260 | 79 of 259 |
| Rash | Skin and subcutaneous tissue disorders | 57 of 260 | 95 of 259 |
| Anaemia | Blood and lymphatic system disorders | 60 of 260 | 83 of 259 |
| Upper Respiratory Tract Infection | Infections and infestations | 69 of 260 | 70 of 259 |
| Constipation | Gastrointestinal disorders | 66 of 260 | 52 of 259 |
Serious events with the highest arm-level rate: pneumonia (22.4%), pyrexia (7.3%), febrile neutropenia (6.2%), atrial fibrillation (5.4%), sepsis (3.9%).
The registry reports serious adverse events and other adverse events as counts among participants at risk. For placebo with bendamustine and rituximab, 157 of 260 participants at risk had a serious adverse event, 255 of 260 had an other adverse event, and 129 deaths are reported. For ibrutinib with bendamustine and rituximab, the corresponding entries are 201 of 259, 256 of 259, and 120 deaths. These are descriptive counts, not adjusted comparisons of risk.
The registry lists pneumonia at 22.4%, pyrexia at 7.3%, febrile neutropenia at 6.2%, atrial fibrillation at 5.4%, sepsis at 3.9%, and cellulitis at 3.5% among the leading serious adverse-event terms. The record does not provide an arm-specific breakdown for these listed terms in the information, nor does it give the definition used for serious adverse events in this summary. The counts and terms should therefore be read as registry safety descriptions, not as proof that a treatment caused an event or as a complete assessment of comparative safety.
18. What the Result Does, and Does Not, Mean
The posted primary analysis shows a progression-free survival comparison that favors the ibrutinib-plus-bendamustine-and-rituximab group in direction: its reported median is longer, and the hazard ratio for Treatment A versus Treatment B is below the no-difference reference. The sponsor reports a 95% confidence interval that remains below that reference and a log-rank p-value of 0.011. These are group-level results for the trial population and the endpoint as defined in the registry.
The result does not mean that every participant in the ibrutinib group remained progression-free longer than every participant in the placebo group. A median is a group summary, and a hazard ratio is a relative event-rate summary over follow-up. Neither gives an individual prediction. The registry also does not report the upper confidence limit for the Treatment B median, which limits interpretation of that particular median’s precision.
The result does not by itself answer all questions about survival, response, quality of life, or safety. Secondary analyses are unadjusted or not reported in the registry, and some analysis details are unavailable. Serious adverse-event counts and deaths are descriptive entries and do not alone establish a causal comparison. The registry record also does not provide enough information to assess every assumption, missing-data procedure, or multiplicity decision.
Accordingly, the posted result supports a statistical comparison of progression-free survival in the randomized groups under the reported analysis. It should not be extended to outcomes, populations, or circumstances not described by the registry, and it is not a substitute for clinical judgment or medical advice.
19. Why This Trial Matters Statistically
This trial illustrates why the endpoint and the statistical summary must be read together. Progression-free survival combines event occurrence and timing, while the median and hazard ratio describe different aspects of the resulting time-to-event data. The median gives a familiar time summary, and the hazard ratio expresses the reported relative comparison across follow-up. Neither should be interpreted as a complete description of every participant’s experience.
It also shows the value of distinguishing a sponsor-reported primary analysis from secondary calculations. The primary result has a stated log-rank method, hazard ratio, confidence interval, and p-value. The secondary risk differences are recalculations from posted percentages, are unadjusted, and have no sponsor-reported analyses listed. Treating those sources as interchangeable would overstate what the registry establishes.
The incomplete upper confidence limit for one reported median, the absence of a reported multiplicity plan, and missing detail on censoring and missing data are practical examples of how registry reporting can constrain statistical interpretation. These are not reasons to discard the posted result, but they are reasons to state precisely which result is being interpreted and where uncertainty remains.
Finally, the planning illustrations emphasize that sample-size requirements depend on the effect targeted and the assumptions used. They are not evidence of observed power and do not reveal the trial’s original design rationale. Separating planning calculations from the trial’s actual reported analysis is essential for sound interpretation.
20. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
Several limitations specific to this registry record affect interpretation. The upper confidence limit for median progression-free survival in the ibrutinib group is not reported, leaving that median’s interval incomplete. Detailed censoring rules, follow-up completeness, and procedures for handling missing outcome data are also not reported in the registry record.
The primary analysis is described as intent-to-treat, but the record does not provide a fuller account of exclusions, protocol deviations, or missing measurements. The registry reports a primary log-rank comparison but does not provide the full statistical analysis plan, including information needed to evaluate model assumptions or planned sensitivity analyses.
The registry lists many secondary outcomes, but it does not report a multiplicity strategy, and sponsor analyses are not listed for the secondary comparisons described by recalculated risk differences. Those recalculations are unadjusted and should not be treated as confirmatory tests. The available numerical results also do not describe every secondary outcome measure listed in the record.
Safety reporting is limited in the information summarized: serious and other adverse-event counts and deaths are listed, but the registry does not provide the arm-specific context for the leading serious-event terms in this record. The trial’s original sample-size justification and interim-analysis details are not reported. These reporting limitations do not change the stated primary estimate, but they restrict independent evaluation of the broader analysis and safety picture.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: A Study of the Bruton's Tyrosine Kinase Inhibitor Ibrutinib Given in Combination With Bendamustine and Rituximab in Patients With Newly Diagnosed Mantle Cell Lymphoma — NCT01776840.
- Registry record last updated 2025-07-08; status last verified 2025-06.
- Results first posted 2022-07-26.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
Continue through the Clinical Biostats statistical pathway
Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
24. Record Summary
The registry describes a completed randomized, double-blind, placebo-controlled phase 3 parallel-group trial in patients 65 years of age or older with newly diagnosed mantle cell lymphoma. It compares ibrutinib plus bendamustine and rituximab with placebo plus bendamustine and rituximab. The primary outcome is progression-free survival, defined by progression, relapse after complete response, or death.
The reported primary analysis gives a hazard ratio of 0.75, a 95% confidence interval from 0.59 to 0.96, and a log-rank p-value of 0.011. The registry reports median progression-free survival of 52.9 months for the placebo group and 80.6 months for the ibrutinib group, with the latter median’s upper confidence limit not reported. Secondary recalculations are unadjusted, and multiplicity and missing-data procedures are not reported in the registry record.